The adjective multidimensional describes anything with many different parts or aspects. You might talk about your relationship with the next door neighbor as multidimensional if, say, he's also your teacher, and if his son is married to your older sister.
Describing something as multidimensional implies that it's complex. You could talk about a multidimensional book filled with intricate themes, characters, plots, and symbols; or you could even call a person multidimensional if she had a particularly complicated personality. The word dimension forms the root of multidimensional, so if you imagine "many dimensions," you'll have a clear idea of what the word means.
adj having or involving or marked by several dimensions or aspects
having dimension--the quality or character or stature proper to a person
2-dimensional, flat, two-dimensional
lacking the expected range or depth; not designed to give an illusion or depth
3-dimensional, third-dimensional, three-d, three-dimensional
involving or relating to three dimensions or aspects; giving the illusion of depth
involving or relating to the fourth dimension or time